Problem 18 - Chemistry The Central Science In Si Units

Question

List the following types of electromagnetic radiation in order of descending wavelength: (a) UV lights used in tanning salons \((300-400 \mathrm{nm}) ;\) (b) radiation from an FM radio station at \(93.1 \mathrm{MHz}\) on the dial; \((\mathbf{c})\) radiation from mobile phones \((450-2100 \mathrm{MHz}) ;(\mathbf{d})\) the yellow light from sodium vapor streetlights; \((\mathbf{e})\) the red light of a light-emitting diode, such as in an appliance's display.

Step-by-Step Solution

Answer

(b), (c), (e), (d), (a)

Step 1: Understand Electromagnetic Spectrum

The electromagnetic spectrum includes all types of electromagnetic radiation ordered by wavelength. Longer wavelengths are associated with lower frequencies and energy, while shorter wavelengths correspond to higher frequencies and energy. This exercise requires ordering various types of radiation by wavelength from longest to shortest.

Step 2: Convert Frequency to Wavelength

The wavelength (lambda)) and frequency (nu)) of electromagnetic radiation are related by the equation \(lambda = frac{c}{nu})\), where \(c\) is the speed of light (approximately \(3 imes 10^8 mathrm{m/s})\). To convert frequency to wavelength, use this formula. For FM radio (b)), with \(93.1 mathrm{MHz})\), the wavelength is \(lambda\approx frac{3 imes 10^8}{93.1 imes 10^6}=3.22 mathrm{m})\). For mobile phones (c)), using the highest frequency 2100 MHz, \(lambda\approx frac{3 imes 10^8}{2100 imes 10^6}\approx .143 mathrm{m})\).

Step 3: Use Known Wavelengths

For UV light (a)), the range is 300-400 nm. Typical yellow sodium vapor light (d)) is about 590 nm, while red light from LEDs (e)) is around 620-750 nm. Since nm (nanometers) and m (meters) are applicable units, recall 1 nm = \(10^{-9} m\).

Step 4: List Wavelengths

When listed by descending wavelength: (b) FM radio (3.22 m or 322000000 nm), (c) mobile phones (.143 m or 143000000 nm), (e) red LED light (620-750 nm), (d) yellow sodium light (590 nm), (a) UV light (300-400 nm).

Step 5: Arrange Wavelengths in Order

Arrange the types of radiation in order of decreasing wavelength: (b) FM radio, (c) mobile phones, (e) red LED light, (d) yellow sodium light, (a) UV light.

Key Concepts

Wavelength

Wavelength is a fundamental concept in understanding electromagnetic radiation. It refers to the distance over which the wave's shape repeats. In simpler terms, imagine the wave as a series of peaks and troughs; the wavelength is the distance from one peak to the next.

• Wavelength is usually measured in meters, but for microscopic waves like UV light, we use nanometers (nm).
• One nanometer equals one billionth of a meter (1 nm = \(10^{-9} m\)).

Wavelength is inversely related to frequency - as the wavelength increases, the frequency decreases. Understanding this relationship helps in comparing different types of electromagnetic waves, such as those mentioned in the original exercise.

Frequency

Frequency measures how often the wave patterns repeat in a second. It is essentially the number of complete wave cycles that pass a given point per second. We express frequency in hertz (Hz), where one hertz represents one cycle per second.

• Higher frequency waves have more cycles per second and are typically more energetic.
• Lower frequency waves are less energetic and have fewer cycles per second.

The frequency of electromagnetic waves is crucial when working with the electromagnetic spectrum, as it determines other properties, like energy, and influences their behavior and use in technology. For instance, FM radio waves, frequently cited in exercises, have specific frequencies that determine how they're received and broadcasted.

Radio Waves

Radio waves are at the long-wavelength end of the electromagnetic spectrum. They are vital for communication technologies like radio, television, and mobile phones. These waves can travel great distances, which is why they are used for broadcasting.

• Radio waves have wavelengths ranging from a few centimeters to over a hundred meters.
• They have lower frequencies and energies compared to other types of electromagnetic waves, like UV light.

FM radio specifically uses radio waves with frequencies between 87.5 MHz to 108 MHz. Such low frequencies allow for clear audio transmissions over large areas. In school exercises, radio waves illustrate how changes in frequency and wavelength affect applications in communication.

UV Light

Ultraviolet (UV) light lies beyond the visible spectrum, next to the violet part of visible light, hence the name "ultraviolet." It encompasses wavelengths from 10 nm to 400 nm. UV light is more energetic than visible light and has many important applications and effects.

• UV radiation is known for causing sunburn, as it can penetrate the skin and cause cellular damage.
• It is also used in sterilization processes, as it can destroy bacteria and viruses.

Supplied in tanning salons, UV light bulbs emit wavelengths between 300 nm to 400 nm. When discussing ordering of electromagnetic waves by wavelength, UV light serves as the shorter-wavelength, higher-energy contrast to radio waves.

Visible Light

Visible light is the range of electromagnetic radiation that can be detected by the human eye. It consists of the spectrum of colors we see, each with different wavelengths ranging approximately from 380 nm (violet) to 750 nm (red).

• Each color in visible light corresponds to a different wavelength, with violet having the shortest and red the longest.
• The perception of these colors results from the different wavelengths interacting with the photoreceptors in our eyes.

Visible light forms a crucial section of the electromagnetic spectrum, bridging the lower-energy infrared and the higher-energy ultraviolet light. In practical exercises, visible light is often referenced through common light sources such as sodium vapor lamps and LEDs, demonstrating the diverse applications of this type of radiation.